Buzzing on unit. I checked the contacts. I cleaned them with emery paper to try and make sure

Question

I checked the contacts. I cleaned them with emery paper to try and make sure there was a good contact. But the buzzing keep on. The buzzing is coming from the brown connector where the contacts are. I am assuming that is the coil? I am guessing I need to replace it since cleaning up the contacts didn't work. Is there something else I should do? If I need to replace it would I need to order the part from a HVAC company or can I get it from a hardware store i.e. Home Depot?